Not quite so - but you do need a richer mixture for a hot start and for a short time afterwards.
A problem with many cars is heat soak when you park with a hot engine and on a hot day. Which can make a big difference to the temperature of the inlet tract etc over a running engine with draws in ambient air, if you attempt a hot start soon afterwards. You may also get a degree of fuel evaporation is the fuel rails. One way round this can be to increase the fuel pressure for a hot start. On my MegaSquirt equipped engine, I also open the fast idle valve setting for hot cranking. As soon as it fires, it goes back to normal. That does seem to suggest I'm giving it too rich a mixture for a hot re-start, but since it works I've left it like that. The big problem with this sort of tuning is getting the conditions exactly the same each time before changing anything - to avoid chasing your tail. ;-)